Uma abordagem usando evolução diferencial para solucionar problemas de programação em dois níveis não lineares

Abstract

Bi-level optimization problems occur in several areas, for example: game theory, control, economics, design, etc. Bi-level optimization problems are considered difficult to solve, especially the nonlinear ones. Many approaches to solve linear, differentiable or convex bi-level problems have been proposed and work with relative efficiency and effectiveness. However, there are few methods for solving nonlinear, non-differentiable and non convex bi-level problems. Many of these methods solve only a subclass of the problem, such as problems with linear constraints or only with the function of the leader being nonlinear. This study proposes a novel approach using Differential Evolution to solve nonlinear bi-level problems in general. In addition, this work develops a method for constraint handling, present in bi-level programming problems. Promising results have been obtained, showing the effectiveness of the approach.